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If each of the 20 bolts of fabric on a shelf is either

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by Gmat_mission » Sun Jun 30, 2019 9:27 am

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If each of the 20 bolts of fabric on a shelf is either 100 percent cotton, 100 percent wool, or a mixture of cotton and wool, how many bolts contain both cotton and wool?

(1) Of the 20 bolts, 18 contain some wool and 14 contain some cotton.
(2) Of the 20 bolts, 6 are 100 percent wool.

[spoiler]OA=A[/spoiler]

Source: Veritas Prep
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Source: — Data Sufficiency |

by deloitte247 » Sat Jul 13, 2019 6:21 am
How many bolts are cotton and wool mixture
Let x = 100% cotton
Let y = 100% wool
Let z = mixture of cotton and wool
x + y + z = 20 find z
Statement 1 => Of the 20 bolts 18 contain some wool and 14 contain some cotton
y + z = 18 and x + z =14
x + y + z = 20
x + 18 = 20
x =2; y =6 and z =12 statement 1 is SUFFICIENT

Statement 2 => Of the 20 bolts 6 are 100% wool
y = 6
x + y + z = 20
x + z = 20 - 6
x + z = 14 value of z remains unknown; statement 2 is NOT SUFFICIENT

Answer = option A as statement 1 alone is SUFFICIENT.
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